Experimental and DEM Analysis on Secondary Crack Types of Rock-Like Material Containing Multiple Flaws Under Uniaxial Compression
Abstract
:1. Introduction
2. Mesoscopic Parameter Calibration and Basic Theory
2.1. Specimen Preparation and Mesoscopic Parameter Calibration
2.2. Strain Rate Tensor
3. Analysis of Numerical Simulation Results
3.1. Research on Crack Propagation Mechanism
- (1)
- The typical characteristics of Type I are described as follows. The directions of horizontal component of particle velocity on both sides of the crack are opposite, the vertical component is in the same direction and the vertical component of the velocity is almost no different or zero. It can be obviously seen that the relative motion tendency of the particle is mainly controlled by the horizontal velocity component.
- (2)
- For Type II, the directions of particle velocity on both sides of the crack are almost the same, and the values have no difference. In this case, the motion trend between the particles has certain inhibitory effects on the crack initiation and propagation.
- (3)
- For Type III, the horizontal and vertical components of the particle velocity on both sides of the crack are the same, but the values are different.
- (4)
- For Type IV, the directions of particle velocity on both sides of the crack are opposite.
3.2. Analysis and Discussions
4. Conclusions
- (1)
- By defining a variable R to quantify the crack failure mechanism, the types and mechanical behaviors of the secondary cracks between the flaws can be effectively distinguished. The initiation mechanism of secondary cracks between flaws is most complicated, and the types and mechanical behaviors of newly generated cracks are distinctive in different stress loading stages. According to the value of variable R, we can directly understand the types mechanical behaviors of secondary cracks.
- (2)
- According to the velocity and relative motion trend of the particles on both sides of the crack, the velocity field of the particles can be obviously divided into four types. The type of particle velocity field on both sides of the newly generated cracks determines the type of crack in the measurement region. At different stress loading stages, the velocity field types of the particles on both sides of the crack are constantly evolving and complicated.
- (3)
- Combined with the particle velocity field analysis and the value of the variable R, it can be seen that the macro tensile crack contains partial shear cracks, and the macro shear crack contains partial tensile cracks, indicating that the type of macro crack is not totally determined by the type of partial cracks. The secondary cracks contain tensile micro-cracks, shear micro-cracks, and compressive-shear micro-cracks, and the number of tensile micro-cracks is the largest. However, when the axial stress is reached to 35.12 MPa, the ratio ( = 22.52) indicates that the newly generated cracks are shear cracks in essence. Therefore, we can see that the type of macro-crack does not depend on the dominant type of micro-cracks.
- (4)
- At the beginning stage of secondary crack initiation, SC-1 and SC-2 appear as shear cracks between pre-existing parallel flaws, then extend up and down toward the tip of the flaws, and finally connect the tips of T2 and T4, as well as T1 and T3, in the form of arcs. The particles between pre-existing parallel flaws form a confined compressive member under uniaxial compression. Under the confinement of lateral particles, the contacts between particles are broken owing to the combined compressive and shear actions, and eventually the shear cracks are successively formed.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Material | Compressive Strength (MPa) | Tensile Strength (MPa) | Young’s Modulus E (GPa) | Poisson’s Ratio | Density (g/cm3) |
---|---|---|---|---|---|
Cement mortar | 58.25 | 5.62 | 11.63 | 0.20 | 2.38 |
Sandstone | 20~170 | 4~25 | 3~35 | 0.02~0.25 | 2.10~2.40 |
Properties | Specimens for Laboratory Tests | Specimens for Numerical Simulation |
---|---|---|
Density (/) | 2.38 | 2.38 |
Young’s modulus E (GPa) | 11.63 | 11.95 |
Poisson’s ratio | 0.20 | 0.21 |
Uniaxial compressive strength (MPa) | 58.25 | 57.30 |
Particle Parameters | Values |
---|---|
Minimum radius (mm) | 0.18 |
Particle radius ratio | 1.66 |
Density (/) | 2.38 |
Friction | 0.55 |
Effective modulus (GPa) | 5.5 |
Normal/shear stiffness ratio | 2.0 |
Tensile strength (MPa) | 22.5 2.0 |
Cohesion (MPa) | 19.5 2.0 |
Angle of internal friction (0) | 35 |
Bond effective modulus (GPa) | 5.5 |
Bond normal/shear stiffness ratio | 2.0 |
Loading Stages | Loading Stresses (MPa) | ||
---|---|---|---|
a | 35.12 | 23.52 | - |
b | 36.96 | 37.77 | - |
c | 37.24 | 35.75 | - |
d | 43.40 | - | 27.53 |
e | 43.61 | - | 41.69 |
f | 45.61 | −45.60 | 23.02 |
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Li, Y.; Cai, W.; Li, X.; Zhu, W.; Zhang, Q.; Wang, S. Experimental and DEM Analysis on Secondary Crack Types of Rock-Like Material Containing Multiple Flaws Under Uniaxial Compression. Appl. Sci. 2019, 9, 1749. https://doi.org/10.3390/app9091749
Li Y, Cai W, Li X, Zhu W, Zhang Q, Wang S. Experimental and DEM Analysis on Secondary Crack Types of Rock-Like Material Containing Multiple Flaws Under Uniaxial Compression. Applied Sciences. 2019; 9(9):1749. https://doi.org/10.3390/app9091749
Chicago/Turabian StyleLi, Yong, Weibing Cai, Xiaojing Li, Weishen Zhu, Qiangyong Zhang, and Shugang Wang. 2019. "Experimental and DEM Analysis on Secondary Crack Types of Rock-Like Material Containing Multiple Flaws Under Uniaxial Compression" Applied Sciences 9, no. 9: 1749. https://doi.org/10.3390/app9091749